Sorry you feel this is out of place... but honestly for most of us this wouldn't be TES without the Dwemer.
Partially. Dwemer tech on Vvardenfel is powered by the Heart of Lorkhan, and hence shuts down when far enough from the power source (or completely, now that the source is gone). However, there are also Dwemer on the mainland and in Hammerfell which use different technologies to power their golems.
http://www.imperial-library.info/content/morrowind-senilius-report (says that the machines from Vvardenfell only seem to work on Vvardenfell, which is assumed to be like that because of the proximity to Red Mountain and the Heart of Lorkhan)
That could be anything, not the Heart of Lorkhan per say.
The Heart is the only thing that makes sense. We know that the Dwemer studied it and harnessed its power, and its the only thing that makes Vvardenfell truly unique.
Gameplay. It'd be boring if all the enemies suddenly died.
The whole point of the report is that they constructs don't function if they are away from Vvardenfell.
I have to agree with Lady of the Sky about it not truly meaning the Heart of Lorkhan mainly because after the destruction of the Heart, the constructs continue to function. However, I believe that the dwemer machinery underground draw magical power from Nirn (Geo-thermal energy) which then the Dwemer cities become founts of magical power to power the constructs. Of course my explanation can't be any more valid than the Heart of Lorkhan theory. However, the constructs in the rest of Tamriel will have to have another source of magic other than the heart of lorkhan but my theory still allows for that power to continue no matter where they are. Your really have to wonder why all those pipes ran along the walls, I believe that they draw magic from the lava from within the earth which is supported by several lava pools showing up in Dwemer ruins.
If we want to delve into a plausible answer that explains the gameplay as well as this account I might have a theory. Lets say, all Dwemer constructs on Vvardenfell get their power from the Heart. Its obvious there are Dwemer ruins and constructs outside Vvardenfell that still operate. We have accounts of ruins on the mainland, there are the constructs under Mournhold, and of course those in Hammerfell. I think its possible that all Dwemer constructs are capable of running off this other power source(geothermal power harnessed at the ruins). So, they still need to be nearby the ruins. Possibly, the Heart allowed the constructs to venture further from their ruins than the normally could have anywhere else. So, when the main power source was removed, all the Dwemer constructs switched back over to running off whatever energy source all other constructs outside of Vvardenfell normally use.
If that is the case, then when the Centurion on its way to Cyrodiil finally went out of range of the Heart, it to probably attempted to run of whatever energy they normally get. However not being near any Dwemer ruins, it could deplete that energy very fast, and so probably instead choose to power down.
This would explain the report and why the constructs still work after the mainquest is completed.